| Logistic | R Documentation |
Density, distribution function, quantile function and random
generation for the logistic distribution with parameters
location and scale.
dlogis(x, location = 0, scale = 1, log = FALSE) plogis(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE) qlogis(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE) rlogis(n, location = 0, scale = 1)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
location, scale |
location and scale parameters. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x]. |
If location or scale are omitted, they assume the
default values of 0 and 1 respectively.
The Logistic distribution with location = m and
scale = s has distribution function
F(x) = 1 / (1 + exp(-(x-m)/s))
and density
f(x) = 1/s exp((x-m)/s) (1 + exp((x-m)/s))^-2.
It is a long-tailed distribution with mean m and variance π^2 /3 s^2.
dlogis gives the density,
plogis gives the distribution function,
qlogis gives the quantile function, and
rlogis generates random deviates.
The length of the result is determined by n for
rlogis, and is the maximum of the lengths of the
numerical arguments for the other functions.
The numerical arguments other than n are recycled to the
length of the result. Only the first elements of the logical
arguments are used.
qlogis(p) is the same as the well known ‘logit’
function, logit(p) = log(p/(1-p)),
and plogis(x) has consequently been called the ‘inverse logit’.
The distribution function is a rescaled hyperbolic tangent,
plogis(x) == (1+ tanh(x/2))/2, and it is called a
sigmoid function in contexts such as neural networks.
[dpq]logis are calculated directly from the definitions.
rlogis uses inversion.
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 2, chapter 23. Wiley, New York.
Distributions for other standard distributions.
var(rlogis(4000, 0, scale = 5)) # approximately (+/- 3) pi^2/3 * 5^2
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